A sonometer wire produces 20 beats per second with a 300 Hz tuning fork. The tension in the wire is then increased by 44%, while its vibrating length and linear density remain unchanged, and the beat frequency becomes 36 beats per second. If the original string frequency is N Hz, find N.
Physics · Wave Motion · beat and properties of sound
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Question

A sonometer wire produces 20 beats per second with a 300 Hz tuning fork. The tension in the wire is then increased by 44%, while its vibrating length and linear density remain unchanged, and the beat frequency becomes 36 beats per second. If the original string frequency is N Hz, find N.

Physics · Wave Motion · beat and properties of sound

G1 Physics · Accepted Answer

Initially, |f−300| = 20. So, f = 280 Hz or 320 Hz. The new tension is T' = 1.44T. Since f ∝ √T, f' = √1.44 f = 1.2f. If f = 280 Hz, then f' = 336 Hz, and the new beat frequency is |336−300| = 36 Hz. If f = 320 Hz, then f' = 384 Hz, and the beat frequency would be 84 Hz. Therefore, N = 280.